Computing Dot Products

Linear Algebra (Matrices) · Axiom Academy

Multiply matching components, sum them, then use the result to find the angle between two vectors. Given and , compute the dot product and use it to find the angle between the two vectors. The dot product is positive, so the vectors lean the same way and the angle θ is acute (less than 90°). Nicely done. You computed a dot product component-by-component and used it to recover the angle between two vectors. Dot product: — multiply matching components, then sum. Watch the signs: a negative component times a positive one gives a negative product; here 8 + (-2) + (-3) = 3 . Sign tells the lean: means (acute); =0 means perpendicular; < 0 means obtuse. The same formula powers projections, work in physics, and orthogonality tests throughout linear algebra.

This is the written version of the interactive lesson above. See the full Linear Algebra (Matrices) course.